Existence and Stability of L4,5 In The Relativistic Restricted Three-Body Problem

The existence and stability of triangular libration points in the relativistic restricted three-body problem has been studied. It is found that L_4,5 are unstable in the whole range 0 ≤ μ ≤ 1/2 in contrast to the classical restricted three-body problem where they are stable for 0 < μ < μ₀, where μ is the mass parameter and μ₀ = 0.03852.... This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling the linear polarization of optical emission from red giants

We present the results of solving the radiative transfer equation for the Stokes vector in the case of light scattering by spherical forsterite dust particles in an axisymmetric circumstellar envelope of a red giant. We have assumed that the surfaces of constant scattering-particle density are prolate or oblate spheroids, the particle density decreases with radius as N _d ∝ r ⁻², and the dust particles at the inner boundary of the envelope are in thermal equilibrium with the stellar emission at solid-phase evaporation temperature T _ev = 800 K. In the wavelength range 0.27 μm ≤ λ ≤ 1 μm, particles with radii 0.03 μm ≲ a ≲ 0.2 μm make a major contribution to the linear polarization of the stellar emission. The increase in scattering efficiency factor with decreasing wavelength λ is mainly responsible for the growth of polarization toward the short wavelengths known from observations. However, at a mean number of scatterings 1.2 ≤ N _sca ≤ 1.6, the polarization ceases to grow due to depolarization effects and decreases rapidly as the wavelength decreases further. The wavelength of the polarization maximum is determined mainly by two quantities: the particle radius and the mass loss rate. The upper limits for the degree of linear polarization in the case of light scattering in circumstellar dust envelopes with the geometries of prolate and oblate spheroids are p ≈ 3 and 5%, respectively. The polarization for light scattering by enstatite particles is higher than that for light scattering by forsterite particles approximately by 0.3%. Original Russian Text ? Yu.A. Fadeyev, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 2, pp. 123–133.     

On the βSPEC Values of Galaxy Clusters During the Merger

Time-dependent, X-ray emission properties of merging subclusters of galaxies are studied by N-body + Hydrodynamic simulations. We consider rather idealized cases, in which two virialized subclusters with the same or different masses collide with each other, eventually merging into one bigger cluster. We find that the various observable quantities, such as the cluster temperature, T_g, the line-of-sight velocity dispersion of galaxies, σ₁, and the specific energy ratio, β_spec ≡ μ m_p σ /k_B T_g (where μ is the mean molecular weight in amu, m_p is the proton mass and k_B is the Boltzmann constant) are distinct in merging clusters from those in isolated clusters. When merging, especially, in addition to having large velocity dispersions, σ_l ≳ 2000 km s^-1, clusters will have large deviations of β_spec from unity; that is, β_spec ≳ 2.0 (or β_spec ≲ 0.5) when seen from the direction parallel (perpendicular) to the collision axis. Temperature profiles are the best indicator of merging process. The calculated temperature maps of merging clusters are compared with those of the observed clusters, such as the Coma cluster, A754, and A401/399 supercluster. These simulated features are in good agreement with what ASCA revealed. Further, we present rather unique features in the temperature profiles that can be caused by a merger (or an encounter) with a subgroup of galaxies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Infrared variability of the nucleus of the Seyfert galaxy NGC 1068 in 1998–2004

Our 8-year-long JHKLM photometry of the Seyfert galaxy NGC 1068 has confirmed its IR variability. The amplitudes of the brightness variations in the J (1.25 μm) and K (2.2 μm) bands are within 0 _. ^m 15 and 0 _. ^m 3, respectively, and exceed the observational errors by more than a factor of 5. The nucleus of NGC 1068 is a variable source and can be at different phases of activity. The brightness of the galaxy in all bands except J decreased from 1998 until 2004. In this period, there was a tendency for the J brightness to increase. The variable source in NGC 1068 is a complex structured object. At least two sources radiate in the wavelength range 1.25–5 μm: a hot source whose radiation shows up in the range 1.25–1.65 μm and a cold source radiating at long wavelengths (2.2–5 μm). The color temperature of the hot source increased from 2300 K (the beginning of our observations) to ∼2700 K (the end of our observations). In contrast, the temperature of the cold source decreased by several tens of degrees (in the temperature range 800–900 K). The IR brightness and color variations observed in 1998–2004 are attributable to the dispersal of the dust envelope that formed around the galactic nucleus some 30 years ago and reached its maximum density in 1994–1995. Our analysis of the spectral energy distributions for the galaxy has shown that the observed radiation in the range 1.25–5 μm can be represented as the sum of radiations from two blackbody sources. For the first period of our observations (JD 2451400), the temperatures of the hot and cold sources are ∼3100 and 760 K, respectively. For the second period (JD 2453230), they are ∼3200 and 720 K, respectively. The hot source is relatively compact; it is smaller in size than the cold source by several tens of times. The mean sizes of the hot and cold sources are ∼2.35 × 10¹⁶ and ∼7.8 × 10¹⁷ cm, respectively. The total mean luminosity of the two sources did not change between the beginning and the end of our observations. The optical depth of the dust envelope averaged over the spectrum of the hot source is τ ∼ 1.5. In 2004, the state of the dust envelope almost returned to its 1974 level, i.e., the dust envelope formation and dispersal cycle was ∼11 000 days (∼30 yr). Original Russian Text ? O.G. Taranova, V.I. Shenavrin, 2006, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2006, Vol. 32, No. 7, pp. 489–496.     

Unusual infrared fading of CH Cygni in 2006

Infrared observations of the unique symbiotic system CH Cyg in 2003–2006 are presented. Analysis of the observations has shown that a fairly dense dust structure (a cloud or a shell) appeared on the line of sight in August–November 2006. The dust grains in the new shell are similar in optical properties to graphite ones and their sizes are mostly within the range 0.14–0.16 μm. The dust shell is optically thick and its optical depth at 2.2 μm is τ(2.2) ≈ 0.97. The dust shell mass is M _d(06) ≈ 8 × 10⁻⁶ M _⊙ and the rate of matter flow into the shell has reached ∼2 × 10⁻⁵ M _⊙ yr⁻¹. Original Russian Text ? O.G. Taranova, V.I. Shenavrin, 2007, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2007, Vol. 33, No. 8, pp. 598–603.     

Stability Regions and Quasi-Periodic Motion in the Vicinity of Triangular Equilibrium Points

The regions of quasi-periodic motion around non-symmetric periodic orbits in the vicinity of the triangular equilibrium points are studied numerically. First, for a value of the mass parameter less than Routh's critical value, the stability regions determined by quasi-periodic motion are examined around the existing families of short (L^s ₄) and long (L^l ₄) period solutions. Then, for two values of μ greater than the Routh value, the unified family L^sl ₄, to which, in these cases, L^s ₄ and L^l ₄ merge, is considered. It is found that such regions surround in general the linearly stable segments of the corresponding families and become smaller as the mass ratio increases. This revised version was published online in July 2006 with corrections to the Cover Date.     

Long term variations in solar flare activity

A statistical analysis of the contemporary (1954-1975) solar flare particle events has been made for the parametersF (integrated, proton fluence in cm^-2 in an event with kinetic energy above 10 MeV) andR ₀ (the characteristic rigidity). These data are compared with the long-term averaged values determined from stable- and radio-nuclide measurements of lunar samples. The analysis shows that the ancient solar flare proton spectrum was harder (higher R₀ values) compared to that observed in contemporary flares. A similar analysis can not be made for the mean long-term averaged flux (ˉJ, cm^-2 S^-1), since the contemporary averages suffer from an uncertainty due to the statistics of a single event. However, the average flux estimates for time durations 〈T〉 exceeding 10³ yr, are free from such uncertainties. The long-term averaged ˉJ values obtained over different time scales (10⁴ - 10⁶ yr) suggest a possible periodic variation in solar flare activity, with enhanced flux level during the last 10⁵ yr. The available data rule out the occurrence of giant flares, with proton fluence exceeding 10¹⁵ cm^-2 during the last million years.     

Effects On the Nutation of the Non-Zonal Harmonics of Third Degree

In this paper, we calculate the coefficients of the nutation for a rigid Earth model due to the C _3m and S _3m (m ≠ 0) harmonics of the geopotential, starting from the Hamiltonian theory as developped by Kinoshita (1977). We show that these coefficients are far from being negligible as given the level of truncation of 0.1 μas which is necessary in the reconstruction of the tables of nutation, and also that their value is very close to that given by Bretagnon et al. (1997). This revised version was published online in July 2006 with corrections to the Cover Date.     

The Limit Problems for the Equation of Oscillations of a Satellite

We consider the ordinary differential equation of the second order, which describes oscillations of a satellite with respect to its mass center moving along an elliptic orbit with eccentricity e. The equation has two parameters: e and μ. It is regular for 0 ≤ e < 1 and singular when e = 1. For 1 we obtain three limit problems. Their bounded solution to the first limit problem form a two-dimensional (2D) continuous invariant set with a periodic structure. Solutions to the second limit problem form 2D and 3D manifolds. The μ-depending families of odd bounded solutions are singled out. One of the families is twisted into a self-similar spiral. To obtain the limit families of the periodic solutions to the original problem match together the odd bounded solutions to the first and the second limit problem. The point of conjunction is described by the third (the basic) limit problem. The limit families are very close to prelimit ones computed in earlier studies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Investigation of the polarization observed in infrared absorption bands in the spectra of protostars

We investigate the linear polarization in the two deepest infrared absorption bands observed in the spectra of protostars, the water-ice band with the center near 3.1 μm and the silicate band with the center near 9.7 μm, using a core-mantle confocal spheroid model with various axial ratios a/b and relative volumes of the core material. We consider the effect of the grain shape, structure, and type (oblate, prolate) as well as the type of grain orientation and its location relative to the incident ray of light and the magnetic field direction on the central wavelengths of the two bands and the polarizability in the bands. We have found that the observed relationships between the polarizability in the bands and the ratio of their optical depths at the band centers can be explained if we choose slightly oblate or prolate particles (a/b ≲2 for the silicate band and 1.3 ≲ a/b ≲ 2 for the ice band). For any type of orientation, the core-mantle confocal spheroid model requires different axial ratios for the ice and silicate bands to account for the observed polarization. We show that picket-fence-oriented particles can explain the observed polarization in the ice band at angles α between the particle rotation axis and the incident ray ≳30° and in the silicate band at any α. Perfectly Davis-Greenstein-oriented particles can explain the observed polarization in the ice band at angles Ω between the line of sight and the magnetic field direction ≳60° and in the silicate band at any Ω. The orientation parameter ζ (imperfect Davis-Greenstein orientation) must be no more than 0.5 (oblate particles) and 0.1 (prolate particles) for the ice band and can be arbitrary for the silicate band. Original Russian Text ? T.V. Zinov’eva, 2006, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2006, Vol. 32, No. 10, pp. 748–766.     

Using the quasar VLBI network for the fundamental time—positioning service of the GLONASS space system

Regular high-precision determinations of the Earth’s orientation parameters (EOPs) on the Quasar VLBI Network were begun in August 2006. The observations are performed within the framework of two national programs: daily sessions at three observatories of the Network to determine all five EOPs (the RU-E program) and 8-h sessions on the Zelenchukskaya-Badary and Svetloe-Badary baselines to determine the Universal Time (the RU-U program). The observations from August 2006 through May 2007 are analyzed. The rms deviations of the EOP values obtained in the RU-E program from the IERS C04 series are 1.1 mas for X _p and Y _p, 37 μs for UT1-UTC, and 0.7 and 0.6 mas for X _c and Y _c, respectively. These results closely match the prospective requirements of GLONASS. The rms deviations of the Universal Times obtained in the RU-U program from the IERS C04 series are 146 μs. We consider the immediate prospects for improving the accuracy of EOP determinations in daily sessions and for implementing the e-VLBI mode for an online determination of the Universal Time. Original Russian Text ? A.M. Finkelstein, E.A. Skurikhina, I.F. Surkis, A.V. Ipatov, I.A. Rakhimov, S.G. Smolentsev, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 66–76.     

Spectral energy distribution of OH megamaser galaxies

The properties of OH megamaser galaxies are analyzed. Using the linear dependence of L _OH on L _FIR and the luminosity function for IR galaxies, the expected number of megamasers is estimated. From observational data at many frequencies (from radio waves to x rays), the spectral energy distributions (SEDs) of 16 objects have been plotted and studied. The SEDs of megamasers have the same form from the radio to the x ray range. Considerable emission is observed in the 3 μm range, which evidently indicates the presence of red giants and supergiants in these objects. Possible reasons for the departure of the slope of the dependence of L _OH on L _FIR from unity are considered. The assumption that collisional pumping may play an important role in the inversion of ground levels of the OH molecule and the saturated gain mechanism in megamasers is confirmed. Translated from Astrofizika, Vol. 42, No. 1, pp. 23–36, January–March, 1999.     

OB stars in the Tycho-2 and 2MASS catalogues

The Tycho-2 proper motions and five-band Tycho-2 and 2MASS photometry for approximately 2.5 million common stars have been used to select OB stars and to determine the extinction and photometric distance for each of them. We have selected 37 485 stars and calculated their reddenings based on their positions in the two-color V _T -H, J-Ks diagrams relative to the zero-age main sequence and the theoretical reddening line for B5 stars. Tests confirm that the selected stars belong to the spectral types O-B with a small admixture of later types. We calculate the extinction coefficient R and its variations with Galactic longitude based on the positions of the selected stars in the two-color B _T -V _T , V _T -Ks diagram. The interstellar extinction for each star is calculated as the product of the reddening found and the coefficient R. The extinction and its variations with Galactic longitude agree well with the extinction based on the model by Arenou et al. (1992). Calibration of the relation between the absolute magnitude and reduced proper motion V _T − + 5 + 5 log μ for Hipparcos stars has allowed us to calculate the absolute magnitudes and photometric distances for the selected stars. The distances found agree with those derived from the Hipparcos parallaxes within 500 pc. The distribution of the stars and the extinction variations with distance found show that the selected stars form an almost complete sample of stars with spectral types earlier than B5 within about 750 pc of the Sun. The sample includes many noticeably reddened stars in the first and second Galactic quadrants that are absent from the Hipparcos and Tycho Spectral Types Catalogues. This slightly changes the pattern of the distribution of OB stars compared to the classical pattern based on Hipparcos. Original Russian Text ? G.A. Goncharov, 2008, published in Pis’ma v Astronomicheskiĭ Zhurnal, 2008, Vol. 34, No. 1, pp. 10–20.     

Variability of Circumstellar Emission from Dust Envelopes Around Carbon Stars

The main constituents of the dust, produced around late-type carbon stars, are thought to be carbon and silicon carbide (SiC), although their exact nature is not yet well established. This subject has been addressed by several authors and good fits of a large number of IRAS sources (chosen among the carbon stars exhibiting the SiC feature at about 11.3 μm) were obtained. In this work we use the same procedure on a limited number of objects, of the same type, taking into account the variability of such sources and the changes induced in their IR spectra. For this purpose, the chosen stars have been observed with a spectral resolution higher than that available for the IRAS data (λ/Δλ ≅ 50), using the CGS3 instrument of the UKIRT telescope, both in the low (λ/Δλ ≅ 160) and in the high (λ/Δλ ≅ 500) resolution configuration. The results are discussed and some preliminary conclusions are drawn. This revised version was published online in September 2006 with corrections to the Cover Date.     

Formation of Dust Grains in Circumstellar Envelopes of Oxygen-Rich AGB Stars

We discuss dust formation in steady state dust driven winds around oxygen-rich AGB stars, including not only homogeneous Al₂O₃ and silicate grains but also heterogeneous grains consisting of an Al₂O₃ core and a silicate mantle. In the inner subsonic region, Al₂O₃ grains with radii of ∼ 0.15 μm condense first, then condensation of silicate on Al₂O₃ starts slightly inside the sonic point, which accelerates the gas flow into the supersonic region. Also small silicate grains, whose radii are a few tens of ?ngstroms form beyond the sonic point. The carrier of 13 μm feature observed towards oxygen-rich AGB stars is considered to be the core-mantle grains consisting of an α-Al₂O₃ core and a silicate mantle from the radiation transfer calculations based on the results of dust formation calculations. This revised version was published online in September 2006 with corrections to the Cover Date.     

Thermal radiation properties of Apollo 14 fines

The thermal radiation properties as a function of bulk density, angle of illumination and wavelength are presented for lunar fines from the Apollo 14 mission. The density range covered is from 1095 kg/m³ to 1590 kg/m³ and a wavelength range of 0.36–14.5 μm. The solar albedo and total emittance were calculated from spectral values and are compared to Apollo 11 and 12 values.     

Time Analysis of the CO+ COMA OF COMET P/HALLEY BY IMAGE PROCESSING TECHNIQUES

Photographic and photoelectric observations of comet P/Halley's ion gas coma from CO⁺ at 4250 ? were part of the Bochum Halley Monitoring Program, conducted from 1986 February 17, to April 17 at the European Southern Observatory on La Silla (Chile). In this spectral range it is possible to watch the continuous formation, motion and expansion of plasma structures. To observe the morphology of these structures 32CO⁺ photos (glass plates) from P/Halley's comet have been analysed. They have a field of view of 28°.6× 28°.6 and were obtained from 1986 March 29, to April 17 with exposure times between 20 and120 minutes. All photos were digitized with a PDS 2020 GM (Photometric Data System) microdensitometer at the Astronomisches Institut derWestf?lischen Wilhelms-Universit?t in Münster (one pixel= 25 μm × 25 μm ≈ 46′.88×46′.88). After digitization the data were reduced to relative intensities, and the part with proper calibrations were also converted to absolute intensities, expressed in terms of column densities using the image data systems MIDAS (Munich Image Data Analysis System; ESO – Image Processing Group, 1988) and IHAP (Image Handling And Processing; Middleburg, 1983). With the help of the Stellingwerf-Theta-Minimum-Method (Stellingwerf, 1978) a period of (2.22 ± 0.09) days results from analysis of structures in the plasma-coma by subtracting subsequent images. This method is also compared with the Fourier method. There may be a second cycle with a period of about 3.6 days. The idea behind subtracting subsequent images is that rotation effects are only 10% phenomena on gas distribution. Difference images are than used to suppress the static component of the gas cloud. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Note on Parameter Values for Stable Low-Inclination Periodic Motion in the Restricted Three-Body Problem with Radiation

The intervals of the mass parameter (μ) values for possible stability of the basic families of 3D periodic orbits in the restricted three-body problem determined elsewhere are now extended into regions of theμ - q ₁ parameter space of the photogravitational restricted three-body problem, where q ₁ is the radiation factor of m ₁ and it is assumed that m ₂ does not radiate. Several 3D periodic orbits corresponding to these regions are computed and tested for stability and seven regions, corresponding to the vertical-critical orbits l1v, l'1v, l6v, m1v, m2v and i1v, survive this stability test, emerging as the regions allowing the simplest types of stable low inclination 3D motion of the infinitesimal particle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tentative Detection of Circumstellar CO2 from the AGB Star R Crateris

We report on and discuss the detection of an emission feature at 14.98 μm from the oxygen-rich, semi-regularly pulsating Asymptotic Giant Branch star R Crateris, a feature which we suggest to be due to the ₀ ¹ Q-branch of circumstellar CO2. We also suggest a reasonable excitation mechanism, which could explain the height, the width and the asymmetry of the feature. This revised version was published online in August 2006 with corrections to the Cover Date.     

Linear stability and the resonance cases for the triangular libration points for the doubly photo-gravitational elliptic restricted problem of three bodies

In the present paper we have found the range of values of μ ande for the linear stability of the triangular points for the doubly photogravitational elliptic restricted problem of three bodies. It has been shown that some resonances of the third and the fourth order exist which will need special investigation for the determination of complete stability of the libration points under our terms of reference.